Duration
45h Th, 30h Pr
Number of credits
| Bachelor in mathematics | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Mathematical analysis is the branch of mathematics concerned with the notion of limit. We will present in this course the concept of limit of a sequence in the complex plane. We will then consider the functions and their properties (continuity, derivation,...).
Mathematical analysis is the branch of mathematics concerned with the concept of limit.
In this course, we will introduce the concept of the limit of a sequence in the complex plane. Subsequently, we will explore functions and their properties, including continuity and differentiation.
Learning outcomes of the learning unit
The aim of this course is to introduce the basic notions and results concerning the mathematical analysis for one variable functions.
This course aims to provide students with the essential analytical foundation for further mathematical studies.
The study of fundamental concepts in analysis (limits, continuity, differentiability) is designed to develop rigorous reasoning and the ability to formulate and justify mathematical arguments.
The course will also help students adapt to a sustained learning pace and cultivate regular independent study, essential for progressively mastering the concepts.
Prerequisite knowledge and skills
Only knowledge in Elementary mathematics is required. Of course, abilities to mathematical reasoning are an asset.
The various topics will be covered comprehensively to allow any student with a solid high-school background to grasp them. Students who have completed a high-school curriculum with a heavy emphasis on mathematics will likely have an advantage throughout the course. A good understanding of basic mathematics is required, and the ability to reason abstractly is an asset.
Planned learning activities and teaching methods
The exercices, directed by the assistants, are mainly dedicated to the resolution of exercises related to the theory taught during the course. They are also useful to obtain supplementary informations and to illustrate concepts tackled during the theoretical course.
The analysis course is structured around two main components.
The first component is theoretical, delivered by the professor in lectures to all students. Attendance at lectures is optional. Students who choose to attend are expected to adhere to basic rules of punctuality, silence, and respect, avoiding unnecessary comings and goings. Some students may prefer to study the material independently at home, combining lecture materials with reference books; this choice is fully respected.
The second component consists of tutorial sessions (TDs or problem-solving sessions), led by teaching assistants. Attendance at these sessions is strongly recommended, as they provide essential preparation for exams. Students are also expected to follow basic rules of punctuality, silence, and respect, which excludes unnecessary comings and goings during the sessions.
Mode of delivery (face to face, distance learning, hybrid learning)
The timetable will be available at the beginning of the academic year. Concerning the exercises, a detailed schedule as well as informations about how the students will be split into groups will be also distributed.
Face-to-face course
Further information:
The analysis course is delivered primarily in person. A detailed schedule will be communicated to students during the orientation day. This schedule may change, so it is recommended to follow its updates regularly.
The tutorial sessions (TDs or problem-solving sessions) aim to illustrate and complement the concepts introduced in lectures. The goal is not to solve exercises mechanically, but to develop understanding and critical thinking regarding mathematical concepts. Students are expected to review the relevant lecture material before the session. This requires little time and will greatly facilitate learning.
Recommended or required readings
There is a reference book. Partial course notes (in french) are also available. The slides will also be made available.
Platform(s) used for course materials:
- eCampus
Further information:
A PDF of the lecture slides will be available on eCampus. Students may supplement these notes during the lecture, which will be more effective if the slides are reviewed briefly beforehand.
The exam material consists of the contents of these slides, supplemented by the professor's comments, additions, and demonstrations, which make up a significant portion of the material. The reference textbook is provided to enhance understanding of the course:
- Samuel Nicolay, Analyse mathématique - Fonctions définies sur une partie de la droite réelle, 2018, ISBN 978-2340024700
Assessment methods and criteria
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions ) AND oral exam
Other : No oral exams for the physical sciences.
Additional information:
Concerning the students in the Mathematic Bachelor Degree. The examination consists of two parts: a written one and an oral one, except for the students attempting the agregation (these will not have any oral part). The written part is devoted to the resolution of problems and exercises. The oral part is devoted to the theory (mainly proofs of theorems) but also includes direct applications of the theory. If a result (considered without decimal numbers) is lower than 8/20 in one of the parts, the lowest result will contribute for two third of the total result. Otherwise, both parts will contribute equally to the final result. The expected knowledge needed for this examination will be officially announced during the year.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions ) AND oral exam
Further information:
The examination consists of a written and an oral part, except for students in the agrégation program, who will only be assessed in writing.
- The written part focuses on solving exercises.
- The oral part covers the theory and its immediate applications.
Additional Information on Examinations:
- Students must present their ULiège student card and identity card at all examinations; failure to do so may result in being denied access.
- The examinations are governed by university regulations, available on the Faculty of Sciences website.
- Students whose mother tongue is not French are allowed to use a dictionary during exams, after obtaining prior approval from the professor.
- Calculators are prohibited during assessments.
Work placement(s)
Organizational remarks
In case of restrictions related to a health crisis, the teaching can be adapted in order to respect the imposed constraints. For example the flipped classroom strategy could be adopted.
Website of the Faculty of Science:
www.sciences.uliege.be
Contacts
S. Nicolay
Institut de Mathématique (B37), Grande Traverse, 12, Sart-Tilman, 4000 Liège.
E-mail : S.Nicolay@uliege.be
Site web : www.afaw.ulg.ac.be
S. Nicolay
Institut de Mathématique (B37), Grande Traverse, 12, Sart-Tilman, 4000 Liège.
E-mail: S.Nicolay@uliege.be
Website: www.afaw.ulg.ac.be
H. Bertrand
E-mail : H.Bertrand@uliege.be
ATTENTION:
- Please use only your ULiège email address (XXX@student.uliege.be) for all communication with the teaching staff.
- Use the title "Student 1BMath..." in your emails.
- Be clear, concise and polite in your messages.
You may, of course, contact us for any questions.